Description
Farmer John goes to Dollar Days at The Cow Store and discovers an unlimited number of tools on sale. During his first visit, the tools are selling variously for $1, $2, and $3. Farmer John has exactly $5 to spend. He can buy 5 tools at $1 each or 1 tool at $3 and an additional 1 tool at $2. Of course, there are other combinations for a total of 5 different ways FJ can spend all his money on tools. Here they are: 1 @ US$3 + 1 @ US$2 1 @ US$3 + 2 @ US$1 1 @ US$2 + 3 @ US$1 2 @ US$2 + 1 @ US$1 5 @ US$1 Write a program than will compute the number of ways FJ can spend N dollars (1 <= N <= 1000) at The Cow Store for tools on sale with a cost of $1..$K (1 <= K <= 100).
Input
A single line with two space-separated integers: N and K.
Output
A single line with a single integer that is the number of unique ways FJ can spend his money.
Sample Input
Sample Output
1 #include<iostream> 2 #include<cstdio> 3 #include<cstring> 4 using namespace std; 5 int max(int &a,int &b){return a>b?a:b;} 6 int n,k; 7 struct bignum{ 8 int a[100],len; 9 bignum(){memset(a,0,sizeof(a));len=0;} 10 void print(){ 11 for(int i=len;i;--i) printf("%d",a[i]); 12 } 13 bignum operator + (const bignum &tmp) const{ 14 bignum c; int x=0; 15 c.len=max(len,tmp.len); 16 for(int i=1;i<=c.len;++i){ 17 c.a[i]=a[i]+tmp.a[i]+x; 18 x=c.a[i]/10; c.a[i]%=10; 19 }for(;x;x/=10) c.a[++c.len]=x%10; 20 return c; 21 } 22 }f[1002]; 23 int main(){ 24 scanf("%d%d",&n,&k); 25 f[0].a[f[0].len=1]=1; 26 for(int i=1;i<=k;++i) 27 for(int j=i;j<=n;++j) 28 f[j]=f[j]+f[j-i]; 29 f[n].print(); 30 return 0; 31 }